The cap is part of an RC network that maintains the low impedance of the shunt reg at high frequencies; without that network the impedance rises and becomes inductive. The values depend mostly on the voltage; at around 300 volts the corner frequency is around 10kHz so the cap is important above that frequency.
Therefor, in theory it should be well-behaved (i.e. with low ESR and ESL) at high frequencies. Initially, I did not expect it to be audible because it's dominated by the resistor except above 10kHz, and because the regulator itself is isolated from the tube by a very high impedance current source plate load. I included it because it should improve the stability margin of the circuit.
Of course, theory is limited in its ability to predict subtle effects that millions of years of evolution have made quite audible. Initially I doubted that it would be audible, but we tested this by substituting a Russian mil-spec teflon capacitor and were startled to find that it did make a small but audible improvement. So I spec a polypropylene capacitor, same as we use for coupling caps.